It is a fundamental problem to understand the complexity of high-accuracy sampling from a
strongly log-concave density π on ℝ d. Indeed, in practice, high-accuracy samplers such as …

We apply the shifted composition rule--an information-theoretic principle introduced in our
earlier work [AC23]--to establish shift Harnack inequalities for the Langevin diffusion. We …

Noisy gradient descent and its variants are the predominant algorithms for differentially
private machine learning. It is a fundamental question to quantify their privacy leakage, yet …

Coupling arguments are a central tool for bounding the deviation between two stochastic
processes, but traditionally have been limited to Wasserstein metrics. In this paper, we apply …

We study the rate at which the initial and current random variables become independent
along a Markov chain, focusing on the Langevin diffusion in continuous time and the …

HWI inequalities are interpolation inequalities relating entropy, Fisher information and
optimal transport distances. We adapt an argument of Y. Wu for proving the Gaussian HWI …

KL (µY∥ νY)≤ KL (µX′∥ νX)+ EKL (µY| X= x∥ νY| X= x′) where µ is a joint distribution
on X, X′, Y; ν is a joint distribution on X, Y; and the expectation is over any coupling (x, x′) …